Constraints on the symmetry energy and neutron skins from experiments and theory

The symmetry energy contribution to the nuclear equation of state impacts various phenomena in nuclear astrophysics, nuclear structure, and nuclear reactions. Its determination is a key objective of contemporary nuclear physics, with consequences for the understanding of dense matter within neutron stars. We examine the results of laboratory experiments that have provided initial constraints on the nuclear symmetry energy and on its density dependence at and somewhat below normal nuclear matter density. Even though some of these constraints have been derived from properties of nuclei while others have been derived from the nuclear response to electroweak and hadronic probes, within experimental uncertainties-they are consistent with each other. We also examine the most frequently used theoretical models that predict the symmetry energy and its slope parameter. By comparing existing constraints on the symmetry pressure to theories, we demonstrate how contributions of three-body forces, which are essential ingredients in neutron matter models, can be determined.

Figure 1

Density dependence of the symmetry energy from the Skyrme interactions used in Ref. 6. The shaded region is obtained from HIC experiments as described in the text and corresponds to the shaded region in Fig. 2.

Figure 2

Constraints on the slope $L$ and magnitude $S_0$ of the symmetry energy at saturation density from different experiments. The experimental methods are labeled next to the boxes with the estimated uncertainties. The symbols are results without the analysis of the errors. See text for details.

Figure 3

Symmetry energy correlations from different models (symbols). The dashed and solid lines represent the linear relationship between $L$ and $S_0$ in the QMC and CEFT models, respectively. The shaded region represents constraints obtained from the HIC experiment. The axes are the same as Fig. 2.

Figure 4

Density dependence of pressure in pure neutron matter as predicted in BHF, QMC, and CEFT models without (left panel) and with (right panel) 3$n$ forces. The inset in the left panel shows experimental data currently available on the neutron skin thickness in ${}^{208}$Pb and the red star indicates their weighted average. For more details see text.